In general one has the following where R_{n} are Rao Uppuluri-Carpenter Numbers (according to OEIS). First few (starting with n=0) are 1, -1, 0, 1, 1, -2, -9, -9, 50, ...pic.twitter.com/joVP3DSed9
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And yes, that is R_{2} = 0. A pretty weird sequence if you ask me... https://oeis.org/A000587 pic.twitter.com/jmF6DaYAJ2
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Touchard polynomials are a interesting connection between the Poisson distribution and stirling numbers of the second kind. Gotta love how all the stuff from special functions pops up either in physics or in stats.pic.twitter.com/0tmjIATuJZ
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K should start with 1
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first term vanishes ;)
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e and pi are endless fun
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